Queueing Delay Analysis for Multicast With Random Linear Coding

We analyze the queueing delay performance when random linear coding is performed over packets randomly arriving at a source node for multicast transmission over packet erasure channels. We model random coding of packets as a bulk-service queueing system, where packets are served and depart the queue in groups. In this framework, we analyze two different block-based random linear coding schemes. The first scheme involves coding over a fixed blocksize, which leads to simpler analysis but also to a delay penalty for lightly-loaded systems. The second scheme adapts to the traffic load by allowing for a variable blocksize, thereby removing the delay penalty at low loads. We provide results on the maximum stable arrival rate of packets at the source and on the queueing delay as a function of the arrival rate.

[1]  M. Medard,et al.  On Delay Performance Gains From Network Coding , 2006, 2006 40th Annual Conference on Information Sciences and Systems.

[2]  Todd Blessinger,et al.  Tunable Approximations for the Mean and Variance of the Maximum of Heterogeneous Geometrically Distributed Random Variables , 2004 .

[3]  R. Koetter,et al.  An Analysis of Finite-Memory Random Linear Coding on Packet Streams , 2006, 2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks.

[4]  Alexandros G. Dimakis,et al.  On the delay of network coding over line networks , 2009, 2009 IEEE International Symposium on Information Theory.

[5]  M. L. Chaudhry,et al.  A first course in bulk queues , 1983 .

[6]  Sanjay Shakkottai,et al.  Looking at Large Networks: Coding vs. Queueing , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[7]  S. Wittevrongel,et al.  Queueing systems , 2019, Autom..

[8]  Chen-Khong Tham,et al.  Minimizing Delay for Multicast-Streaming in Wireless Networks with Network Coding , 2009, IEEE INFOCOM 2009.

[9]  Parimal Parag,et al.  Queueing Analysis of a Butterfly Network for Comparing Network Coding to Classical Routing , 2010, IEEE Transactions on Information Theory.

[10]  Anthony Ephremides,et al.  A queueing model for random linear coding , 2007, MILCOM 2007 - IEEE Military Communications Conference.

[11]  Utpal Mukherji,et al.  Stability of Scheduled Message Communication over Degraded Broadcast Channels , 2006, 2006 IEEE International Symposium on Information Theory.

[12]  Milica Stojanovic,et al.  Random linear network coding for time-division duplexing: Queueing analysis , 2009, 2009 IEEE International Symposium on Information Theory.

[13]  A. Ephremides,et al.  On the queueing delay of a multicast erasure channel , 2006, 2006 IEEE Information Theory Workshop - ITW '06 Chengdu.

[14]  R. Koetter,et al.  The benefits of coding over routing in a randomized setting , 2003, IEEE International Symposium on Information Theory, 2003. Proceedings..

[15]  Anthony Ephremides,et al.  Stable Throughput for Multicast With Random Linear Coding , 2011, IEEE Transactions on Information Theory.

[16]  Angela I. Barbero,et al.  Improved delay estimates for a queueing model for random linear coding for unicast , 2009, 2009 IEEE International Symposium on Information Theory.

[17]  Erol Gelenbe,et al.  Queueing performance under Network Coding , 2009, 2009 IEEE Information Theory Workshop on Networking and Information Theory.

[18]  Robert B. Cooper,et al.  Queueing systems, volume II: computer applications : By Leonard Kleinrock. Wiley-Interscience, New York, 1976, xx + 549 pp. , 1977 .

[19]  Leonard Kleinrock,et al.  Queueing Systems: Volume I-Theory , 1975 .

[20]  G. J. A. Stern,et al.  Queueing Systems, Volume 2: Computer Applications , 1976 .

[21]  C. D. Litton,et al.  A First Course in Bulk Queues , 1983 .